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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Find the equation of the xy-trace of the sphere given by

( x + 1 ) 2 + ( y 2 ) 2 + ( z + 3 ) 2 = 5 2 .

To determine

To calculate: The equation of the xy-trace of the sphere whose equation is (x+1)2+(y2)2+(z+3)2=52.

Explanation

Given Information:

The equation of sphere, x2+y2+z2+6x8y+2z10=0.

Formula used:

The intersection of the one of the three co-ordinate planes with surface to visualize the surface. Such intersection is called a trace of the surface.

Calculation:

Consider the equation of sphere,

(x+1)2+(y2)2+(z+3)2=52

The xy-trace means the intersection of the surface with xy-plane. Since, at xy-plane the z-coordinate will be zero

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